QuestionA bacteria culture starts with 3000 bacteria. After 3 h , the estimated count is 48000 . What is the doubling period? $$d=?$$

Studdy Solution
Calculate the doubling period $d$ using the growth rate $r$.
The formula for the doubling period is: $$d = \frac{\ln(2)}{r}$$
Substitute the value of $r$ from the previous step: $$d = \frac{\ln(2)}{\frac{\ln(16)}{3}}$$ $$d = \frac{3 \cdot \ln(2)}{\ln(16)}$$
Since $\ln(16) = 4 \cdot \ln(2)$, we simplify: $$d = \frac{3 \cdot \ln(2)}{4 \cdot \ln(2)}$$ $$d = \frac{3}{4}$$
The doubling period is: $$\boxed{\frac{3}{4}} \text{ hours}$$